Sensation and Analysis of the Differential Reynolds Stress Modell SSG/LRR-omega for flows with mean-streamline curvature using local Richardson number

Kurzfassung

The present study focuses on the effects of streamline curvature in curved turbulent boundary layers. Bradshaw’s gradient Richardson number was used to identify zones of convex and concave curvatures. A Galilean-invariant version of Richardson number (Ri-local) augmented by the direction information of Spalart & Shur’s rotation/curvature correction framework was derived. The behaviour of the Richardson number was investigated by conducting a sensitivity study by parameterizing the Monson’s U-duct test case for varying curvature magnitude. The capability of Ri-local to identify the sign and magnitude of curvature is demonstrated for different curvature magnitudes of U-duct test case. Suitable test cases (both convex and concave curvature) from the experiments in the literature namely Monson (1990), Gillis & Johnston (1981) and So & Mellor (1972) were chosen. The geometries were built and CFD setups were developed and validated using RANS models. Using the validation cases, rotation/curvature corrections to SA, SST were compared and the SSG/LRR-omega was assessed for convex and concave curvatures. It was determined that SSG/LRR-omega gives better agreement with the experimental data than SA-RC and SST-RC for the convex curved turbulent boundary layers. For the concave curvature test case, SSG/LRR-omega gives a good agreement with the trough region of Taylor-Görtler vortex where effects of these longitudinal vortices are minimal. The double peak structure of Reynolds shear stress in longitudinal vortices on a concave wall was not captured by any of the RANS models in the present work. Moreover, different redistribution models namely Speziale-Sarkar-Gatski (SSG), Launder-ReeceRodi (LRR) and SSG/LRR-omega were compared for convex and concave curvatures where SSG/LRR-omega gives the best agreement with the experimental profiles of mean-velocity, Reynolds shear stress and Reynolds stress anisotropy. The Generalized Gradient Diffusion Hypothesis (GGDH) and the Simple Gradient Diffusion Hypothesis (SGDH) were examined for both convex and concave turbulent boundary layers. GGDH gives better agreement with the experimental data compared to SGDH for different Reynolds stress models. Based on the insights from the validation cases, prospects for curvature sensitsation of SSG/LRR-omega were explored. Modifications to the turbulent transport term using the Rilocal were investigated based on the comments from Zeman. Trials were conducted to modify the production of length scale, thus modifying dissipation thereby and further changing the production of Reynolds shear stress. Insights into further modification of SSG/LRR-omega for complex flows were provided.